The high symmetry points with \(\delta k=\pi \)  in the BZ are the PH symmetric points, and we expect the quantum phase transition to be dominated by the behavior near these points. Hence, we must ensure the simulation includes the effects of these high-symmetry points, in order to efficiently determine the phase diagram, which we do by the symmetry-enforced quantum circuits discussed above. Using these specific momenta for the larger systems discussed in Fig. REF , we obtain the entanglement entropy (from the same correlation function as above) as a function of exchange parameter, shown in Fig. REF . Although the bond fermion entanglement entropy does not fully capture the system entanglement entropy, the portion that comes from the gauge fermions is featureless [1]}, and thus sharp transitions may be found by studying the bond fermions alone.
